The 21-year-old centre-half, who played for Corby Town in 2012-2013, follows hot-on-the-heels of fellow arrivals Ashley Timms and Gary Mills.
Piergianni, who played for the Pilgrims’ Centre of Excellence during his teenage years, made his Football League debut as a Peterborough player in 2010.
He made 44 appearances for Stockport County during the 2011-2012 Blue Square Bet Premier campaign (scoring four goals in the process).
Piergianni also enjoyed brief loan spells with Spalding United and Altrincham during his Peterborough days.
United boss Dennis Greene told bufc.co.uk: "Carl represents another piece of the jigsaw we are putting together.
"He is a commanding and solid centre-half and has a good pedigree, so we are looking forward to working with him once pre-season gets under way."